1. Field of the Invention
The invention relates generally to global positioning system devices and navigation receivers and more specifically to systems for guiding aircraft through turns.
2. Description of the Prior Art
An airplane's turn rate is reliably proportional to the roll angle and inversely proportional to the airspeed, turnrate=tan(roll)*g/TAS, where TAS is true airspeed and g is the acceleration of gravity, that is, 9.8 m/s.sup.2. Pilots traditionally hold a constant roll angle until their airplanes reach the desired heading or course. A turn from one leg of a flight plan to the next leg is often made by an educated guess by the pilot of the roll angle and the appropriate distance from the intersection that will carry the aircraft to a tangent on the new leg. Such a turn consequently describes a segment of circle within the airmass. However the wind causes the aircraft to vector off such course at a constant speed and direction. The general result is a path over the ground that is a segment of a cycloid, or trochoid. A truly circular arc therefore can only result in the special case of no wind when the turn rate is held constant.
Conventional computerized navigation systems can continuously determine aircraft positions relative to the ground, and can therefore guide aircraft along the established airways and radials from radio-navigation aids. Such systems can also provide guidance along any arbitrary path that may be desired. But such systems make turns with simple curves that are commonly laid out as arcs of circles relative to the ground, and are not necessarily circular relative to the airmass.
In the prior art systems where wind is considered, the information is used only to find the sharpest turn radius possible that does not exceed the roll angle capability of the airplane. That part of the turn that is most nearly downwind often involves the greatest roll angles. Unless there is no wind, the consequence of using a circular model is that the roll angle must vary throughout the turn. The whole of such turns will never be as sharp as they could be if a maximum roll angle could have been maintained throughout the turning.
When plenty of airspace is available, gentler turns may be executed. But even in this case, a circular turning strategy generally requires a larger than necessary roll angle during some part of the turn.
What the prior art lacks is a capable navigation system for making guided turns that use constant roll angles. For example, to stay within limited airways and the limits of allowable roll angle, or to turn with as little roll angle as possible within the space available. Such a constant roll through a turn is needed to assure passengers who would otherwise become concerned about frequent banking changes.